Abstract
We demonstrate that an idea related to the Central Limit Theorem and approximations by accompanying laws in probability theory is useful to get optimal convergence rates in some approximation formulas for operators. As examples we provide a bound for Euler approximations of bounded holomorphic semigroups; a bound for error in approximation of a power of operators by accompanying exponents, which is a useful tool in analysis of the Trotter–Kato formula, and can be considered as an extended version of Chernoff's ‘\(\sqrt n \) lemma’.
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Bentkus, V., Paulauskas, V. Optimal Error Estimates in Operator-Norm Approximations of Semigroups. Letters in Mathematical Physics 68, 131–138 (2004). https://doi.org/10.1023/B:MATH.0000045552.97035.87
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DOI: https://doi.org/10.1023/B:MATH.0000045552.97035.87